Preheat oven to 375 degrees. Line two baking sheets with parchment paper; set aside.
Place 1 1/2 cups of pecan halves in a food processor. Pulse until coarsely ground, but be sure not to process for too long - you don't want the nuts to turn into a paste. Set aside.
In a large bowl, stir together the sugar and melted butter. Beat in the egg and vanilla extract, then add the ground pecans and the flour. Mix well.
To form the cookies, scoop out 1 tablespoon of dough and roll it into a ball, then flatten slightly into a round cookie. Place cookies on the prepared baking sheets, spacing about 2 inches apart. Lightly press a pecan half into the center of each cookie.
Bake 9-11 minutes, until lighten golden around the edges. Remove from the oven and allow to cool for 1-2 minutes on the baking sheet before moving to a cooling rack to cool completely. Once cool, dust with powdered sugar.
Cookies will keep for up to a week in an airtight container, or longer in the freezer...not that they'll last that long.